For the linear function f(x) = mx + b, f(-2) = 11 and f(3) = -9. Find m and b.

Q: The gradient of the line 4y 4 6x is?

A: The gradient of the line = (change in y-coordinate)/(change in x-coordinate) . Gradient of line =…

Q: If f(x) = 4x + 14, find the slope of the secant line between the values of *₁ = 9 and ₂ = 2.

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Q: or the linear function ​f(x)=mx+​b, ​f(−3​)=24​, and ​f(2​)=−6. Find m and b.

A: We can find the value of m and b as below.

Q: If f(x) = 25x + 15, find the slope of the secant line between the values of x1 - 7 and x2 = 6.

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Q: For the function f(x.y) = e 4xy, find f, and f,. f, =

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Q: If f(x) = 24x + 12, find the slope of the secant line between the values of æ1 = - 1 and æ2 2.

A: The slope of the secant line of f(x) between the values x1 and x2 is referred to as the average rate…

Q: For the function y = ax3 +bx2 +cx , there is a point of inflection at (1,-3) and the slope of the…

A: We find the second derivative using the power rule Given that, at x=1 there is a point of…

Q: If f(x) = 24x + 12, find the slope of the secant line between the values of x₁ = - 1 and ₂ = = 2.

A: Topic = Function

Q: Decide which of the two given functions is linear, and find its equation. -10 10 20 30 f(x) -1.5 1.5…

A: The table is, x -10 0 10 20 30 f(x) -1.5 0 1.5 3.5 4.5 g(x) -9 -4 1 6 11   The slope of…

Q: The gradient of the line  8y = 4 - 12 is

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Q: 2X + 5YZ  is NOT a linear function. True False

A: In general the linear function can be written as fx=mx+b where m is slope and b is intercept. The…

Q: For the graph of the linear function f(x) = mx + b, m is the  _____ and b is the _______ .

A: For the graph of the linear function fx=mx+b, m is the  _____ and b is the _____.

Q: For the linear function f(x) = mx +b, f(- 6) = 19, and f(3) = 1. Find m and b. ..... m =

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Q: Answer the following 3 questions using the linear function y=-4x+3 If x = -11 then….. As x -> -∞ As…

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Q: If f(x) = 19x + 22, find the slope of the secant line between the values of xj = 9 and x2 = 3.

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Q: A landscaping company charges $49 per cubic yard of mulch plus a delivery charge of $27. Find a…

A: Given A landscaping company charges  per cubic yard= $49 delivery charge =$27

Q: Find a linear equation satisfying the condition, if possible. y = 101 Passes through (-1, 1) and (4,…

A: lines

Q: If f(x)=25x+25, find the slope of the secant line between the values of x1=4 and x2=10

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Q: Suppose a certain home improvement outlet knows that the monthly demand for framing studs is 2,500…

A: It is given that the demand for farming studs is 2,500 when the price is $4.75 and the demand is…

Q: . Write a rule for a linear function y = h(x), given that h(1) = 6 and h(-3) = 2.

A: Our Aim is to write a rule for a linear function y=h(x), given thath(1)=6 and h(-3)=2

Q: Decide which of the two given functions is linear and find its equation. 0 3 6 10 15 f(x) 35 57 84…

A: Solution : We know a linear function can be of the form, y=ax+b ,here a,b are constants. Now let us…

Q: Decide which of the two given functions is linear and find its equation. ‹ 0 1 2 3 4 f(x) 912 15 18…

A: To find which of the given function is linear (f(x) or g(x)) . Also find its equation :-

Q: Find the slope of the line satisfying f(-1) = 9 and f(1) = - 4.

A:

Q: Given the utility function of a consumer for the goods x and y, U = (x + 2)(y+ 1) and the prices of…

A: According to the given information, it is required to find the optimal levels of purchase x and y.

Q: Find the equation of the linear function, f, which is the perpendicular bisector of the line segment…

A:

Q: Determine whether there exists a constant c such that the line ex - 2y = 4:  (a) Has slope 4…

A: a) We write the line in the y=mx+b form first  Given that slope=c/2=4  So, c=8  Answer(a): Yes, c=8…

Q: Consider the linear function y = ax + b. If x changes at a constant rate, does y change at a…

A:

Q: Find an equation for the linear function g(z) which is perpendicular to the line 7z – 6y = 12 and…

A: Given the equation of a line 7x−6y=12

Q: It is given that the yearly cost of tuition and requires fees for attending a public four-year…

A: Given, Linear function of cost: f(x)=291.5x+2944.05 Slope of the function f(x) is f'(x)

Q: For the linear function f(x)= -2x-2. Describe the line slat

A: The given linear function is: fx=-2x-2

Q: The x-intercept of the linear function f(x) = 4x + 16 is %3D -0.55 O-20.52 O 13.24 O -4.00 O 1.80

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Q: The gradient of the line 4y =4 - 6x  is?

A:

Q: Find the constants m and b in the linear function f(x) = mx + b so that f(9) = 6 and the straight…

A:

Q: The gradient of the line 2y =4 - 3x  is?

A: General form of equation of line is Y=mx+c m=slope=Gradient, C is the intercept on axis Now 2y=4-3x…

Q: for y if y"= 8x – 3 and the slope i

A: Integration: y''=8x-3Integrating both sides we get,y'=8x22-3x+cy'=4x2-3x+c

Q: When a bus pass from Albuquerque to Los Alamos is priced at p dollars, a bus company takes in a…

A: (a)

Q: If ax2+2hxy+by2=0 represents two straight lines such that the slope of online is twice the slope of…

A:

Q: Let f be the linear function  f(x) = −6x + 7. a) wha is The rate of change of f ? b)and what is The…

A: f(x) = −6x + 7 We need a) what is The rate of change of f(x)? b)what is The graph of f and slope and…

Q: Find the equation of line (L) that passes through the intersection point of the two functions y = v2…

A: Need to find the line which is perpendicular to the given line and passes through the intersection…

Q: Suppose that a manufacturer determines that there is a linear relation between P, the profit earned…

A: We know that,

Q: represents

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Q: Decide which of the two given functions is linear and find its equation. 6. 10 15 f(x) 0 3 23 37 54…

A:

Q: If f(x)=9x+3f(x)=9x+3, find the slope of the secant line between the values of x1=−9x1=-9 and…

A:

Q: Suppose a certain home improvement outlet knows that the monthly demand for framing studs is 2,500…

A: Given, Monthly demand for farming studs is 2500 when the price is $ 5 Monthly demand for farming…

Q: f(x)=13x+8, find the slope of the secant line between  x1= -8 and  x2= -9

A: Solution: The objective is to find the slope of the secant line

Q: If f(x) = 15x +3, find the slope of the secant line between the values of x1 5 and x2 = 3. %3D

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Q: Find the equation of the linear function p that has p(4)=8 and that is parallel to h(u)=−3/10u+6.

A:

Q: If ax +2hxy+by 0 represents two straight lines such that the slope of one %3D line is twice the…

A: We have to prove that

Q: Find the extreme value of the function f(x,y) x + y3 - 3x - 12y + 20.

A: To find extreme points of the function f(x,y) we put fx=0 and fy=0. Then we put the extreme points…

Transformation of Graphs

The word ‘transformation’ means modification. Transformation of the graph of a function is a process by which we modify or change the original graph and make a new graph.

Exponential Functions

The exponential function is a type of mathematical function which is used in real-world contexts. It helps to find out the exponential decay model or exponential growth model, in mathematical models. In this topic, we will understand descriptive rules, concepts, structures, graphs, interpreter series, work formulas, and examples of functions involving exponents.